I'm currently painting a window and door that are both new. Although I initially bought primer which I used on the window (but haven't painted over yet), when doing the door, I just used my paint/primer.
I only did the front part of the door this way, and then realized maybe I've made a mistake? Is the paint/primer not good enough on its own? Or can I continue painting the door with just that, and then do a second coat to ensure full coverage?
The paint/primer should be fine, especially with two coats, but I typically begin with primer, as it seems (in my experience) that primer holds paint better and lasts a bit longer before requiring touch ups or repainting, and it's often cheaper to do a coat of good primer (match latex to latex, or make sure you follow the label if you use a different combo), then two or three even coats of less-expensive paint (paint+primer is almost always 2-3x more expensive than paint alone.
I wouldn't sand and re-paint, of course. You should be fine with what you have so far.
[Edit: one other note on paint+primer paints; make sure you read reviews or ask others about their experiences with the particular brand you're buying. A friend ended up with a patchy-looking paint job when he used one of the cheaper brands. I don't know if it was an isolated incident or if the brand is normally bad (or if he didn't mix the paint well!), but research before you buy.]
For once, Wikipedia has a good article on primers: http://en.wikipedia.org/wiki/Primer_(paint)
In summary, paint has two functions: protection and decoration. Primer is really good at protection, so it makes sense to prime properly, with a specialist primer. Combined primer/undercoats inevitably compromise somewhere, usually on the ability to penetrate the wood.
The finish coat is just that, it's for the decoration.
If it's an outside wooden door I'd definitely go for a full three- or four-coat treatment. A good, expensive, aluminium primer, followed by one or two coats of undercoat, followed by one or two coats of top-coat. (But I live in the UK where conditions are horrid for wood -- very rainy, occasionally snowy, and dry and hot in the summer.)
In your case: you'll most likely be OK with two or three coats of combined paint/primer but be prepared for it to need another coat in three or four seasons. At that point a sand/recoat should be good.
Final tips: don't economise on paint quality, expensive brands invariably cover better and last longer. And, match manufacturers and chemistry if at all possible, as a paint "system" that matches will generally last longer. And, prepare, prepare, prepare!
In my opinion any exterior bare wood or wood that will be hit, touched, etc..often should be covered with an oil primer if you have access to it. Allow it to cure properly and then go over it with the topcoat of your choice.
I would definitely prime the wood first. I've had nothing but bad experiences with the paint/primer combos, even the expensive one's. I live in a rural area and am limited in what I can get and I keep finding myself in conflict with clients over this issue. They've fallen for the gimmick that you can do the whole thing in two coats. Not true and like someone else said a third coat of the more expensive PP combo in order to get it to look right is actually costing people more money. That's the gimmick. I wish the stuff would just disappear from the market.
